Stow, S.R and Duck, P.W and Hewitt, R.E
(2001)
*Three-dimensional extensions to Jeffery–Hamel flow.*
Fluid Dynamics Research, 29.
pp. 25-46.

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## Abstract

We consider two viscous ows, both of which are in a class of three-dimensional ow states that are closely related to the classical Je eryâ��Hamel solutions. In the Ã¿rst conÃ¿guration, we consider a ow between two planes, intersecting at an angle , and driven by a line-source-like solution in the neighbourhood of the apex of intersection (just as in classical, two-dimensional, Je eryâ��Hamel ow). However, in addition we allow for a ow in the direction of the line of intersection of the planes (in order to capture the broader class of three-dimensional solutions). In this ow, two solution scenarios are possible; the Ã¿rst of these originates as a bifurcation from Je eryâ��Hamel ow, whilst the second scenario describes a radial velocity of the classical Je eryâ��Hamel form (also with a zero azimuthal velocity component), but with an axial velocity determined from the radial ow. Both of these solutions are exact within the Navierâ��Stokes framework. In the second conÃ¿guration, we consider the high Reynolds number, three-dimensional ow in a diverging channel, with (generally) non-straight walls close to a plane of symmetry, and driven by a pressure gradient. Similarity solutions are found, and a connection with Je eryâ��Hamel ows is established for the particular case of a ow through straight (but non-parallel) channel walls, and again, additional three-dimensional solutions are found. One member of this general class (corresponding to the ow through a straight-walled channel, driven by linearly increasing pressure in both the axial and cross-channel directions), leads to a further family of exact Navierâ��Stokes solutions.

Item Type: | Article |
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Uncontrolled Keywords: | Jeffery-Hamel self-similar exact reduction three-dimensional |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 47 Fluid dynamics |

Depositing User: | Dr Richard E. Hewitt |

Date Deposited: | 14 Nov 2013 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2049 |

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